 In random matrix theory, Dyson [1]} introduced symmetric, hermitian and symplectic matrix-valued processes having matrix entries as independent Ornstein-Uhlenbeck processes, and he derived the stochastic differential equations (SDEs for short) that their eigenvalue processes satisfy:
\(d\lambda _i(t)=\sqrt{\frac{2}{\beta }}dB_i(t)+\sum _{j(\ne i)}\frac{1}{\lambda _i(t)-\lambda _j(t)}dt-\frac{\lambda _i(t)}{2}dt,\ \ i=1,\dots ,N,\) 
